Dilation and Parallel Triangles

Mr. Murphy designed a new logo for the NHS math team. Part of the logo includes a pair of similar triangles as shown in the figure below.

• The center of dilation for these triangles must be one of the vertices of the outside triangle.

• The center of dilation for these triangles must be one of the vertices of the inside triangle.

• The center of dilation for these triangles must be in the interior of the two triangles.

• The center of dilation for these triangles must be exterior to the two triangles.

If line segment AB is dilated about center P by a scale factor of ½ to form A’B’, which statement(s) is/are true? Choose all that apply.

• AB and A’B’ are parallel. 

• A’B’ is twice as long as AB. 

• The endpoints of A’B’ are ½ the distance to P as the endpoints of AB. 

Find the missing length.

• 6

• 8

• 5

• None of these

Find the missing length.

• 21

• 18

• 16

• 24

Which proportion would be correct in order to solve for x.  (Hint: remember the side splitter theorem states the sides of the triangles are proportional)

• x/10 = 15/30

• x/10 = 45/30

• x/10 = 15/45

• x/10 = 30/15

A dilation is which of the following: 

• only an enlargement

• only a reduction

• Either an enlargement or a reduction

• Neither an enlargement or a reduction

The point A (8, 12) was dilated to become point A' (2, 3). What was the scale factor?

• ½

• ¼

• 4

• 2

Choose the correct scale factor:

• 2

• 3

• 1/3

• 1/2

State the coordinate of the image of the given point G (-10,-6) under a dilation with center at the origin with the given scale factor of 1/2.

• G' (5,3)

• G' (20,12)

• G' (-20,-12)

• G' (-5,-3)